{"id":41858,"date":"2017-06-03T10:52:52","date_gmt":"2017-06-03T07:52:52","guid":{"rendered":"https:\/\/new.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/"},"modified":"2019-06-24T17:33:14","modified_gmt":"2019-06-24T14:33:14","slug":"3-lxx-2017","status":"publish","type":"post","link":"https:\/\/vocedu.azbuki.bg\/en\/matematics\/matharticles2016-2\/3-lxx-2017\/","title":{"rendered":"Mathematics and Informatics, Number 3\/2017, Volume 60"},"content":{"rendered":"

<\/a>CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><\/p>\n

\u00a0<\/p>\n

EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418<\/strong>
\u0412\u044a\u0440\u0445\u0443 \u0435\u0434\u0438\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0434\u043e\u043c\u0430\u0448\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0430 \u043d\u0430 \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <\/a>
[On a Model of the Homework in the Context of Self-Preparation in Mathematics Education] <\/a>
\/ \u041c\u0430\u0440\u0433\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Marga Georgieva, Diana Stefanova \u2013 \u0441\u0442\u0440.\/page 231
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\u00a0<\/p>\n

\u041d\u044f\u043a\u043e\u043b\u043a\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u041c\u0435\u043d\u0435\u043b\u0430\u0439 \u0437\u0430 \u0432\u043f\u0438\u0441\u0430\u043d\u0438 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438 <\/a>
[Some Applications of Menelaus Theorem to Inscribed Circles] <\/a>
\/ \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0430 \u0419\u043e\u0432\u043a\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0425\u0440\u0438\u0441\u0442\u043e\u0432\u0430, \u041b\u0438\u043b\u0438 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Alexandra Yovkova, Irina Hristova, Lilly Stefanova \u2013 \u0441\u0442\u0440.\/page 243
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\u00a0<\/p>\n

EDUCATIONAL TECHNOLOGIES \/ \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u0422\u0415\u0425\u041d\u041e\u041b\u041e\u0413\u0418\u0418<\/strong>
\u0412\u0442\u043e\u0440\u0438 \u043f\u0441\u0435\u0432\u0434\u043e\u0446\u0435\u043d\u0442\u044a\u0440 \u043d\u0430 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430 <\/a>
[Second Pseudocenter of the Quadrilateral] <\/a>
\/ \u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432 \/ Stanislav Stefanov \u2013 \u0441\u0442\u0440.\/page 252
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\u00a0<\/p>\n

\u041d\u044f\u043a\u043e\u043b\u043a\u043e \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438, \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u0434\u043e \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f <\/a>
[Several Problems for Circles Tangent to Conics] <\/a>
\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov \u2013 \u0441\u0442\u0440.\/page 262
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\u041f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u043d\u0430 \u0435\u0434\u0438\u043d \u043d\u043e\u0432 \u043f\u043e\u0434\u0445\u043e\u0434 \u043f\u0440\u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u0435\u043d \u0441\u043e\u0444\u0442\u0443\u0435\u0440 <\/a>
[Application of a New Approach to Educational Software Modeling] <\/a>
\/ \u041c\u0438\u043b\u0435\u043d \u0417\u0430\u043c\u0444\u0438\u0440\u043e\u0432 \/ Milen Zamfirov \u2013 \u0441\u0442\u0440.\/page 274
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\u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u043d\u0438 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0438 \u0432 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0430\u0446\u0438\u044f\u0442\u0430 \u043d\u0430 \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0438 \u043d\u0430 \u0431\u044a\u0434e\u0449\u0438\u0442\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u0438 <\/a>
[\u0415ducational Platforms in the Organization of Pedgogical Practice for Future Teachers] <\/a>
\/ \u041a\u0440\u0430\u0441\u0438\u043c\u0438\u0440 \u0425\u0430\u0440\u0438\u0437\u0430\u043d\u043e\u0432, \u041d\u0430\u0442\u0430\u043b\u0438\u044f \u041f\u0430\u0432\u043b\u043e\u0432\u0430 \/ Krasimir Harizanov, Natalia Pavlova \u2013 \u0441\u0442\u0440.\/page 285
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\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 <\/a>
[National Mathematical Olympiad for University Students] <\/a>
\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Rosen Nikolaev, Veselin Nenkov \u2013 \u0441\u0442\u0440.\/page 291
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\u0411\u0435\u043b\u0435\u0436\u043a\u0430 \u0432\u044a\u0440\u0445\u0443 \u0435\u0434\u043d\u0430 \u043e\u0442 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u0437\u0430 VII \u043a\u043b\u0430\u0441 \u2013 22 \u043c\u0430\u0439 2017 \u0433. <\/a>
[A Note on One of the Problems for 7th Grade \u2013 May 22, 2017] <\/a>
\/ \u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432, \u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432 \/ Sava Grozdev, Veselin Nenkov \u2013 \u0441\u0442\u0440.\/page 295
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\u0413\u0435\u043d\u043d\u0430\u0434\u0438\u0439 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d: \u0441\u043a\u0440\u043e\u043c\u043d\u044b\u0439 \u043f\u043e\u0440\u0442\u0440\u0435\u0442 \u0432 \u0438\u043d\u0442\u0435\u0440\u044c\u0435\u0440\u0435 \u044d\u043f\u043e\u0445\u0438 (\u043a 80-\u043b\u0435\u0442\u0438\u044e \u0441\u043e \u0434\u043d\u044f \u0440\u043e\u0436\u0434\u0435\u043d\u0438\u044f) <\/a>
[Genadii Lukankin: a Modest Picture in the Interior of the Epoch (on Occasion of the 80-Anniversary)] <\/a>
\/ \u0411\u043e\u0440\u0438\u0441 \u0422\u0435\u0431\u0438\u0435\u0432, \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d \/ Boris Tebiev, Alexander Lukankin \u2013 \u0441\u0442\u0440.\/page 299
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\u0421\u043f\u043e\u043c\u0435\u043d \u0437\u0430 \u043f\u0440\u043e\u0444\u0435\u0441\u043e\u0440 \u0410\u043d\u0442\u043e\u043d \u0428\u043e\u0443\u0440\u0435\u043a <\/a>
[A Memory of Professor Anton Shourek] <\/a>
\/ \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0430 \u0422\u0440\u0438\u0444\u043e\u043d\u043e\u0432\u0430 \/ Aleksandra Trifonova \u2013 \u0441\u0442\u0440.\/page 308
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\u00a0<\/p>\n

CONTEST PROBLEMS \/ \u041a\u041e\u041d\u041a\u0423\u0420\u0421\u041d\u0418 \u0417\u0410\u0414\u0410\u0427\u0418<\/strong>
Contest Problems of this Issue
[Contest Problems of this Issue] \u2013 \u0441\u0442\u0440.\/page 317<\/p>\n

\u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0431\u0440\u043e\u0439 4, 2016
[Solutions of the Contest Problems from Issue 4, 2016] \u2013 \u0441\u0442\u0440.\/page 319
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\u00a0<\/p>\n

READ IN THE LATEST ISSUES OF \u201eAZBUKI\u201c JOURNALS \/ \u0412 \u041d\u041e\u0412\u0418\u0422\u0415 \u0411\u0420\u041e\u0415\u0412\u0415 \u041d\u0410 \u0421\u041f\u0418\u0421\u0410\u041d\u0418\u042f\u0422\u0410 \u041d\u0410 \u0418\u0417\u0414\u0410\u0422\u0415\u041b\u0421\u0422\u0412\u041e \u201e\u0410\u0417\u0411\u0423\u041a\u0418\u201c \u0427\u0415\u0422\u0415\u0422\u0415<\/strong><\/p>\n

\u00a0<\/p>\n

GUIDE FOR AUTHORS \/ \u0423\u041a\u0410\u0417\u0410\u041d\u0418\u042f \u0417\u0410 \u0410\u0412\u0422\u041e\u0420\u0418\u0422\u0415<\/strong><\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u0412\u042a\u0420\u0425\u0423 \u0415\u0414\u0418\u041d \u041c\u041e\u0414\u0415\u041b \u041d\u0410 \u0414\u041e\u041c\u0410\u0428\u041d\u0410 \u0420\u0410\u0411\u041e\u0422\u0410 \u0412 \u041a\u041e\u041d\u0422\u0415\u041a\u0421\u0422\u0410 \u041d\u0410 \u0421\u0410\u041c\u041e\u0421\u0422\u041e\u042f\u0422\u0415\u041b\u041d\u0410\u0422\u0410 \u0420\u0410\u0411\u041e\u0422\u0410 \u0412 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u0415\u0422\u041e \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/span><\/strong><\/p>\n

\u00a0<\/p>\n

\u041c\u0430\u0440\u0433\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u0440\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430 \u0435\u0434\u0438\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0434\u043e\u043c\u0430\u0448\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043a\u043e\u043d\u0442\u0435\u043a-\u0441\u0442\u0430 \u043d\u0430 \u0441\u0430\u043c\u043e\u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0430\u0442\u0430. \u041a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044f\u0442\u0430, \u043a\u043e\u044f\u0442\u043e \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u043c\u0435, \u0438\u043c\u0430 \u043f\u0440\u0435\u0442\u0435\u043d\u0446\u0438\u0438 \u0434\u0430 \u0438\u0433\u0440\u0430\u0435 \u0440\u043e\u043b\u044f\u0442\u0430 \u043d\u0430 \u0441\u0442\u0440\u0430\u0442\u0435\u0433\u0438\u044f \u0437\u0430 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435 \u043d\u0430 \u043d\u044f\u043a\u043e\u0438 \u043e\u0442 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438\u0442\u0435 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430.
Keywords:<\/em> mathematics education; self-preparation; homework<\/p>\n

\u00a0<\/p>\n

ON A MODEL OF THE HOMEWORK IN THE CONTEXT OF SELF-PREPARATION IN MATHEMATICS EDUCATION<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The paper considers a model of the homework in the context of self-preparartion. The proposed conception claims a role of a strategy in solving some of the problems in Mathematics education.<\/p>\n

\u00a0<\/p>\n

Prof. Dr. Marga Georgieva
Emeritus Professor
Sofia, Bulgaria<\/p>\n

\u00a0<\/p>\n

Dr. Diana Stefanova
Teacher in Mathematics
Asenovgrad, Bulgaria<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u041d\u042f\u041a\u041e\u041b\u041a\u041e \u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u042f \u041d\u0410 \u0422\u0415\u041e\u0420\u0415\u041c\u0410\u0422\u0410 \u041d\u0410 \u041c\u0415\u041d\u0415\u041b\u0410\u0419 \u0417\u0410 \u0412\u041f\u0418\u0421\u0410\u041d\u0418 \u041e\u041a\u0420\u042a\u0416\u041d\u041e\u0421\u0422\u0418<\/strong><\/p>\n

\u00a0<\/p>\n

\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0430 \u0419\u043e\u0432\u043a\u043e\u0432\u0430, \u0418\u0440\u0438\u043d\u0430 \u0425\u0440\u0438\u0441\u0442\u043e\u0432\u0430, \u041b\u0438\u043b\u0438 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430
Mathematics High School \u2013 Lovech<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0437\u0430\u0434\u0430\u0447\u0438, \u0441\u0432\u044a\u0440\u0437\u0430\u043d\u0438 \u0441 \u0434\u043e\u043f\u0438\u0440\u043d\u0438\u0442\u0435 \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u0432\u043f\u0438\u0441\u0430\u043d\u0438\u0442\u0435 \u0432 \u0442\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438. \u041e\u0441\u043d\u043e\u0432\u0435\u043d \u0435\u043b\u0435\u043c\u0435\u043d\u0442 \u0432 \u0440\u0435\u0448\u0430\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u0435\u0437\u0438 \u0437\u0430\u0434\u0430\u0447\u0438 \u0435 \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 \u043d\u0430 \u041c\u0435\u043d\u0435\u043b\u0430\u0439. \u0420\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0430\u0442\u0430 \u0435 \u043e\u0442\u043b\u0438\u0447\u0435\u043d\u0430 \u0441\u044a\u0441 \u0437\u043b\u0430\u0442\u0435\u043d \u043c\u0435\u0434\u0430\u043b \u043d\u0430 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0438\u044f \u043a\u043e\u043d\u043a\u0443\u0440\u0441 \u201e\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u043f\u0440\u043e\u0435\u043a\u0442\u0438\u0440\u0430\u043d\u0435\u201c \u0432 \u041c\u043e\u0441\u043a\u0432\u0430, \u0420\u0443\u0441\u0438\u044f \u043f\u0440\u0435\u0437 \u043c. \u043c\u0430\u0439 2017 \u0433.
Keywords:<\/em> Menelaus theorem; circle; center; triangle; tangent<\/p>\n

\u00a0<\/p>\n

SOME APPLICATIONS OF MENELAUS THEOREM TO INSCRIBED CIRCLES<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> Several problems are considered in connection with the tangent points of circles inscribed in a triangle. A basic instrument in the problem solving is the application of Menelaus theorem. The work is awarded golden medal in the International competition \u201cMathematics and Projecting\u201d in Moscow, Russia in May 2017.<\/p>\n

Ms. Alexandra Yovkova, Ms. Irina Hristova, Ms. Lilly Stefanova
Mathematics High School \u2013 Lovech (Bulgaria)<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

<\/a>\u0412\u0422\u041e\u0420\u0418 \u041f\u0421\u0415\u0412\u0414\u041e\u0426\u0415\u041d\u0422\u042a\u0420 \u041d\u0410 \u0427\u0415\u0422\u0418\u0420\u0418\u042a\u0413\u042a\u041b\u041d\u0418\u041a\u0410<\/span><\/strong><\/p>\n

\u00a0<\/p>\n

\u0421\u0442\u0430\u043d\u0438\u0441\u043b\u0430\u0432 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432
Technical university \u2013 Sofia<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0430 \u0435\u0434\u043d\u0430 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0430 \u0442\u043e\u0447\u043a\u0430 \u0432 \u0438\u0437\u043f\u044a\u043a\u043d\u0430\u043b \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a \u2013 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u0438\u0435 \u043d\u0430 \u0446\u0435\u043d\u0442\u044a\u0440\u0430 \u043d\u0430 \u043e\u043f\u0438\u0441\u0430\u043d\u0430\u0442\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442 \u043d\u0430 \u0432\u043f\u0438\u0441\u0430\u043d\u0438\u044f \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a. \u0420\u0430\u0437\u0433\u043b\u0435\u0434\u0430\u043d\u0438 \u0441\u0430 \u0432\u0440\u044a\u0437\u043a\u0438\u0442\u0435 \u045d \u0441 \u0434\u0440\u0443\u0433\u0438 \u0437\u0430\u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0435\u043b\u043d\u0438 \u0442\u043e\u0447\u043a\u0438 \u0432 \u0447\u0435\u0442\u0438\u0440\u0438\u044a\u0433\u044a\u043b\u043d\u0438\u043a\u0430.
Keywords:<\/em> quadrilateral; notable point; Euler Circle; Lemoin point; Brocardian circle<\/p>\n

\u00a0<\/p>\n

SECOND PSEUDOCENTER OF THE QUADRILATERAL<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The paper describes some properties of a notable point in convex quadrilateral \u2013 a generalization of the circumcenter of the inscribed quadrilateral.<\/p>\n

\u00a0<\/p>\n

Mr. Stanislav Stefanov, Phd Student
Technical University \u2013 Sofia (Bulgaria)<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u041d\u042f\u041a\u041e\u041b\u041a\u041e \u0417\u0410\u0414\u0410\u0427\u0418 \u0417\u0410 \u041e\u041a\u0420\u042a\u0416\u041d\u041e\u0421\u0422\u0418, \u0414\u041e\u041f\u0418\u0420\u0410\u0429\u0418 \u0421\u0415 \u0414\u041e \u041a\u041e\u041d\u0418\u0427\u041d\u0418 \u0421\u0415\u0427\u0415\u041d\u0418\u042f<\/strong><\/p>\n

\u00a0<\/p>\n

\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432,
University of Finance, Business and Entrepreneurship<\/p>\n

\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432,
\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0420\u0430\u0437\u0433\u043b\u0435\u0436\u0434\u0430\u0442 \u0441\u0435 \u043d\u044f\u043a\u043e\u043b\u043a\u043e \u0437\u0430\u0434\u0430\u0447\u0438 \u0437\u0430 \u043e\u043a\u0440\u044a\u0436\u043d\u043e\u0441\u0442\u0438, \u0434\u043e\u043f\u0438\u0440\u0430\u0449\u0438 \u0441\u0435 \u0434\u043e \u043a\u043e\u043d\u0438\u0447\u043d\u0438 \u0441\u0435\u0447\u0435\u043d\u0438\u044f \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 \u0432\u044a\u0440\u0445\u0443 \u0434\u0438\u0440\u0435\u043a\u0442\u0440\u0438\u0441\u0430\u0442\u0430 \u043d\u0430 \u043a\u043e\u043d\u0438\u0447\u043d\u043e\u0442\u043e \u0441\u0435\u0447\u0435\u043d\u0438\u0435.
Keywords:<\/em> circle; conic; parabola; ellipse; hyperbola; center; triangle; focus; directress<\/p>\n

\u00a0<\/p>\n

SEVERAL PROBLEMS FOR CIRCLES TANGENT TO CONICS<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> Several problems are considered for circles which are tangent to conics and are determined by points on the directress of the conic.<\/p>\n

\u00a0<\/p>\n

Prof. Sava Grozdev, DSc.
University of Finance, Business and Entrepreneurship (Bulgaria)<\/p>\n

Dr. Veselin Nenkov, Assoc. Prof.
Technical College, Lovech (Bulgaria)<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u041f\u0420\u0418\u041b\u041e\u0416\u0415\u041d\u0418\u0415 \u041d\u0410 \u0415\u0414\u0418\u041d \u041d\u041e\u0412 \u041f\u041e\u0414\u0425\u041e\u0414 \u041f\u0420\u0418 \u041c\u041e\u0414\u0415\u041b\u0418\u0420\u0410\u041d\u0415 \u041d\u0410 \u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u0415\u041d \u0421\u041e\u0424\u0422\u0423\u0415\u0420<\/strong><\/p>\n

\u00a0<\/p>\n

Milen Zamfirov
Sofia University<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0421\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u043e\u043f\u0438\u0441\u0432\u0430 \u043f\u0440\u0438\u043b\u0430\u0433\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043d\u043e\u0432 \u043c\u043e\u0434\u0435\u043b \u043f\u0440\u0438 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435\u0442\u043e \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u0435\u043d \u0441\u043e\u0444\u0442\u0443\u0435\u0440. \u041d\u0430\u043f\u0440\u0430\u0432\u0435\u043d \u0435 \u0430\u043d\u0430\u043b\u0438\u0437 \u043d\u0430 \u043d\u0430\u0439-\u0447\u0435\u0441\u0442\u043e \u0438\u0437\u043f\u043e\u043b\u0437\u0432\u0430\u043d\u0438\u0442\u0435 \u043c\u043e\u0434\u0435\u043b\u0438, \u043a\u0430\u0442\u043e \u0431\u043b\u043e\u043a-\u0441\u0445\u0435\u043c\u0438\u0442\u0435 \u0438 \u0423\u043d\u0438\u0444\u0438\u0446\u0438\u0440\u0430\u043d\u0438\u044f \u0435\u0437\u0438\u043a \u0437\u0430 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435, \u043a\u0430\u0442\u043e \u043d\u0430 \u0431\u0430\u0437\u0430\u0442\u0430 \u043d\u0430 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u0442\u043e \u0435 \u043e\u043f\u0438\u0441\u0430\u043d \u0438 \u0441\u0435\u043c\u0430\u043d\u0442\u0438\u0447\u043d\u0438\u044f\u0442 \u043c\u043e\u0434\u0435\u043b \u0437\u0430 \u043c\u043e\u0434\u0435\u043b\u0438\u0440\u0430\u043d\u0435 \u043d\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u0435\u043b\u0435\u043d \u0441\u043e\u0444\u0442\u0443\u0435\u0440.
Keywords:<\/em> educational software modeling; block-modeling schemes; universal modelling language<\/p>\n

\u00a0<\/p>\n

APPLICATION OF A NEW APPROACH TO EDUCATIONAL SOFTWARE MODELING<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The paper describes the application of a new model to educational software modeling. The mostly used models are analyzed such as block-schemes and the Unified language for modeling. Based on comparison, the semantic model of educational software modeling is described too.<\/p>\n

Dr. Milen Zamfirov, Assoc. Prof.
Department of Special Education and Speech Therapy
Sofia University (Bulgaria)<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

<\/a>\u041e\u0411\u0420\u0410\u0417\u041e\u0412\u0410\u0422\u0415\u041b\u041d\u0418 \u041f\u041b\u0410\u0422\u0424\u041e\u0420\u041c\u0418 \u0412 \u041e\u0420\u0413\u0410\u041d\u0418\u0417\u0410\u0426\u0418\u042f\u0422\u0410 \u041d\u0410 \u041f\u0415\u0414\u0410\u0413\u041e\u0413\u0418\u0427\u0415\u0421\u041a\u0418\u0422\u0415 \u041f\u0420\u0410\u041a\u0422\u0418\u041a\u0418 \u041d\u0410 \u0411\u042a\u0414\u0415\u0429\u0418\u0422\u0415 \u0423\u0427\u0418\u0422\u0415\u041b\u0418<\/span><\/strong><\/p>\n

\u00a0<\/p>\n

\u041a\u0440\u0430\u0441\u0438\u043c\u0438\u0440 \u0425\u0430\u0440\u0438\u0437\u0430\u043d\u043e\u0432, \u041d\u0430\u0442\u0430\u043b\u0438\u044f \u041f\u0430\u0432\u043b\u043e\u0432\u0430
\u0428\u0443\u043c\u0435\u043d\u0441\u043a\u0438 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u0415\u043f\u0438\u0441\u043a\u043e\u043f \u041a. \u041f\u0440\u0435\u0441\u043b\u0430\u0432\u0441\u043a\u0438\u201c<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d\u0430 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u043d\u0430 \u0443\u0435\u0431 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430, \u0441 \u043f\u043e\u043c\u043e\u0449-\u0442\u0430 \u043d\u0430 \u043a\u043e\u044f\u0442\u043e \u043c\u043e\u0433\u0430\u0442 \u0434\u0430 \u0441\u0435 \u043e\u0440\u0433\u0430\u043d\u0438\u0437\u0438\u0440\u0430\u0442 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0442\u0435 \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u043d\u0430 \u0431\u044a\u0434\u0435\u0449\u0438\u0442\u0435 \u0443\u0447\u0438\u0442\u0435\u043b\u0438. \u041f\u043e\u043a\u0430\u0437\u0430\u043d\u0438 \u0441\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0442\u0435 \u0440\u043e\u043b\u0438 \u0438 \u0442\u0435\u0445\u043d\u0438\u0442\u0435 \u043f\u0440\u0430\u0432\u0430 \u0432 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430\u0442\u0430. \u041f\u043e\u0441\u043e\u0447\u0435\u043d\u0438 \u0441\u0430 \u043d\u044f\u043a\u043e\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0438. \u0414\u0430\u0434\u0435\u043d\u0438 \u0441\u0430 \u0438\u0434\u0435\u0438 \u0437\u0430 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0438 \u0431\u044a\u0434\u0435\u0449\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u043d\u0430 \u043f\u043b\u0430\u0442\u0444\u043e\u0440\u043c\u0430\u0442\u0430.
Keywords:<\/em> training; electronic resource; didactic design; platform<\/p>\n

\u00a0<\/p>\n

\u0415DUCATIONAL PLATFORMS IN THE ORGANIZATION OF PEDGOGICAL PRACTICE FOR FUTURE TEACHERS<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The paper presents a realization of a web platform, which can be used to organize practical lessons for future teachers. The main roles and their rights in the platform are shown. Some problems are mentioned. Ideas are given for application and future development of the platform.<\/p>\n

\u00a0<\/p>\n

Dr. Krasimir Harizanov, Assist. Prof.; Dr. Natalia Pavlova, Assoc. Prof.
Shumen University (Bulgaria)<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u041d\u0410\u0426\u0418\u041e\u041d\u0410\u041b\u041d\u0410 \u0421\u0422\u0423\u0414\u0415\u041d\u0422\u0421\u041a\u0410 \u041e\u041b\u0418\u041c\u041f\u0418\u0410\u0414\u0410 \u041f\u041e \u041c\u0410\u0422\u0415\u041c\u0410\u0422\u0418\u041a\u0410<\/strong><\/p>\n

\u00a0<\/p>\n

\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432,
University of Finance, Business and Entrepreneurship<\/p>\n

\u0420\u043e\u0441\u0435\u043d \u041d\u0438\u043a\u043e\u043b\u0430\u0435\u0432,
University of Economics \u2013 Varna<\/p>\n

\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432,
\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u041e\u0442 18 \u0434\u043e 22 \u043c\u0430\u0439 2017 \u0433. \u0432 \u043a\u0443\u0440\u043e\u0440\u0442\u0430 \u201e\u041f\u0430\u043c\u043f\u043e\u0440\u043e\u0432\u043e\u201c \u0441\u0435 \u043f\u0440\u043e\u0432\u0435\u0434\u0435 \u0442\u0440\u0430\u0434\u0438\u0446\u0438\u043e\u043d\u043d\u0430\u0442\u0430 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0441\u043a\u0430 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0441 \u043c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u043e \u0443\u0447\u0430\u0441\u0442\u0438\u0435. \u0414\u043e\u043c\u0430\u043a\u0438\u043d \u043d\u0430 \u0441\u044a\u0431\u0438\u0442\u0438\u0435\u0442\u043e \u0431\u0435\u0448\u0435 \u041f\u043b\u043e\u0432\u0434\u0438\u0432\u0441\u043a\u0438\u044f\u0442 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u201e\u041f. \u0425\u0438\u043b\u0435\u043d\u0434\u0430\u0440\u0441\u043a\u0438\u201c. \u0412 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u0430\u0442\u0430 \u0443\u0447\u0430\u0441\u0442\u0432\u0430\u0445\u0430 \u043f\u043e\u0432\u0435\u0447\u0435 \u043e\u0442 100 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u043e\u0442 14 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u043e\u0442 \u0411\u044a\u043b\u0433\u0430\u0440\u0438\u044f \u0438 2 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0430 \u043e\u0442 \u0447\u0443\u0436\u0431\u0438\u043d\u0430. \u0421\u044a\u0441\u0442\u0435\u0437\u0430\u043d\u0438\u0435\u0442\u043e \u043f\u0440\u043e\u0442\u0435\u0447\u0435 \u0432 3 \u0433\u0440\u0443\u043f\u0438 \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442 \u043e\u0442 \u0443\u0447\u0435\u0431\u043d\u043e\u0442\u043e \u0441\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430, \u0438\u0437\u0443\u0447\u0430\u0432\u0430\u043d\u043e \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u0438\u0442\u0435 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0438. \u0412 \u0441\u0442\u0430\u0442\u0438\u044f\u0442\u0430 \u0441\u0435 \u043e\u0431\u0441\u044a\u0436\u0434\u0430\u0442 \u0437\u0430\u0434\u0430\u0447\u0438\u0442\u0435 \u043e\u0442 \u0442\u0440\u0435\u0442\u0430\u0442\u0430 \u0433\u0440\u0443\u043f\u0430. \u0412 \u0442\u0430\u0437\u0438 \u0433\u0440\u0443\u043f\u0430 \u0441\u0435 \u0441\u044a\u0441\u0442\u0435\u0437\u0430\u0432\u0430\u0445\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0438 \u043e\u0442 \u0438\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u0438\u0441\u0448\u0438 \u0443\u0447\u0438\u043b\u0438\u0449\u0430, \u0432 \u043a\u043e\u0438\u0442\u043e \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0435 \u0441 \u043c\u0430\u043b\u044a\u043a \u0431\u0440\u043e\u0439 \u0447\u0430\u0441\u043e\u0432\u0435. \u041f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438 \u0441\u0430 \u043c\u0435\u0442\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.
Keywords:<\/em> problem; solution; Olympiad; University; student<\/p>\n

\u00a0<\/p>\n

NATIONAL MATHEMATICAL OLYMPIAD FOR UNIVERSITY STUDENTS<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The traditional National mathematical Olympiad for University students took place in Pamporovo resort from 18 to 21 May 2017. The event was hosted by the Plovdiv University \u201cP. Hilendarski\u201d. More than 100 students participated in the Olympiad representing 14 Universities from Bulgaria and 2 Universities from abroad. The competition was organized in 3 groups depending on the mathematical curriculum in different Universities. The paper discusses the problems of the third group, in which students from Economics Universities study Mathematics with small number of classes. Methodological solutions are proposed.<\/p>\n

\u00a0<\/p>\n

Prof. Sava Grozdev, DSc.
University of Finance, Business and Entrepreneurship \u2013 Sofia (Bulgaria)<\/p>\n

Dr. Rosen Nikolaev, Assoc. Prof.
University of Economics \u2013 Varna (Bulgaria)<\/p>\n

Dr. Veselin Nenkov, Assoc. Prof.
Technical College – Lovech (Bulgaria)<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u0411\u0415\u041b\u0415\u0416\u041a\u0410 \u0412\u042a\u0420\u0425\u0423 \u0415\u0414\u041d\u0410 \u041e\u0422 \u0417\u0410\u0414\u0410\u0427\u0418\u0422\u0415 \u0417\u0410 VII \u041a\u041b\u0410\u0421 \u2013 22 \u041c\u0410\u0419 2017 \u0413.<\/strong><\/p>\n

\u00a0<\/p>\n

\u0421\u0430\u0432\u0430 \u0413\u0440\u043e\u0437\u0434\u0435\u0432,
University of Finance, Business and Entrepreneurship<\/p>\n

\u0412\u0435\u0441\u0435\u043b\u0438\u043d \u041d\u0435\u043d\u043a\u043e\u0432,
\u0422\u0435\u0445\u043d\u0438\u0447\u0435\u0441\u043a\u0438 \u043a\u043e\u043b\u0435\u0436 \u2013 \u041b\u043e\u0432\u0435\u0447<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u041f\u043e\u0432\u043e\u0434 \u0437\u0430 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0431\u0435\u043b\u0435\u0436\u043a\u0430 \u0435 \u0437\u0430\u0434\u0430\u0447\u0430 24 \u043e\u0442 \u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e\u0442\u043e \u0432\u044a\u043d\u0448\u043d\u043e \u043e\u0446\u0435\u043d\u044f\u0432\u0430\u043d\u0435 \u0437\u0430 VII \u043a\u043b\u0430\u0441, \u043f\u0440\u043e\u0432\u0435\u0434\u0435\u043d\u043e \u043d\u0430 22 \u043c\u0430\u0439 2017 \u0433.
Keywords:<\/em> problem; solution; 7th grade; national assessment<\/p>\n

\u00a0<\/p>\n

A NOTE ON ONE OF THE PROBLEMS FOR 7th GRADE \u2013 MAY 22, 2017<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong>The present note is on the occasion of Problem 24 from the National external assessment for 7th grade held on May 22, 2017.<\/p>\n

\u00a0<\/p>\n

Prof. Sava Grozdev, DSc.
University of Finance, Business and Entrepreneurship \u2013 Sofia (Bulgaria)<\/p>\n

Dr. Veselin Nenkov, Assoc. Prof.
Technical College – Lovech (Bulgaria)<\/p>\n

\u00a0\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>\n

<\/a>\u0413\u0415\u041d\u041d\u0410\u0414\u0418\u0419 \u041b\u0423\u041a\u0410\u041d\u041a\u0418\u041d: \u0421\u041a\u0420\u041e\u041c\u041d\u042b\u0419 \u041f\u041e\u0420\u0422\u0420\u0415\u0422 \u0412 \u0418\u041d\u0422\u0415\u0420\u042c\u0415\u0420\u0415 \u042d\u041f\u041e\u0425\u0418<\/strong>
(\u041a 80-\u043b\u0435\u0442\u0438\u044e \u0441\u043e \u0434\u043d\u044f \u0440\u043e\u0436\u0434\u0435\u043d\u0438\u044f)<\/strong><\/p>\n

\u0411\u043e\u0440\u0438\u0441 \u0422\u0435\u0431\u0438\u0435\u0432,
\u041c\u0435\u0436\u0434\u0443\u043d\u0430\u0440\u043e\u0434\u043d\u0430\u044f \u043f\u0435\u0434\u0430\u0433\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0430\u043a\u0430\u0434\u0435\u043c\u0438\u044f \u2013 \u041c\u043e\u0441\u043a\u0432\u0430<\/p>\n

\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d,
\u041c\u043e\u0441\u043a\u043e\u0432\u0441\u043a\u0438\u0439 \u0440\u0435\u0433\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u0441\u043e\u0446\u0438\u0430\u043b\u044c\u043d\u043e-\u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u2013 \u041c\u043e\u0441\u043a\u0432\u0430<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u0412 \u044d\u0442\u043e\u043c \u0433\u043e\u0434\u0443 \u0438\u0441\u043f\u043e\u043b\u043d\u0438\u043b\u043e\u0441\u044c 80 \u043b\u0435\u0442 \u0441\u043e \u0434\u043d\u044f \u0440\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0413\u0435\u043d\u043d\u0430\u0434\u0438\u044f \u041b\u0430\u0432\u0440\u043e\u0432\u0438\u0447\u0430 \u041b\u0443\u043a\u0430\u043d\u043a\u0438\u043d\u0430 (1937\u2013 2006), \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0433\u043e \u0443\u0447\u0435\u043d\u043e\u0433\u043e-\u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 (\u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043b\u0435\u043a\u0441\u043d\u044b\u0439 \u0430\u043d\u0430\u043b\u0438\u0437, \u043a\u0440\u0430\u0435\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438), \u0432\u0438\u0434\u043d\u043e\u0433\u043e \u0441\u043f\u0435\u0446\u0438\u0430\u043b\u0438\u0441\u0442\u0430 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0441\u0440\u0435\u0434\u043d\u0435\u0433\u043e (\u043e\u0431\u0449\u0435\u0433\u043e) \u0438 \u0432\u044b\u0441\u0448\u0435\u0433\u043e \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f, \u0447\u043b\u0435\u043d\u0430-\u043a\u043e\u0440\u0440\u0435\u0441\u043f\u043e\u043d\u0434\u0435\u043d\u0442\u0430 \u0420\u0410\u041e. \u0413\u0435\u043d\u043d\u0430\u0434\u0438\u0439 \u041b\u0430\u0432\u0440\u043e\u0432\u0438\u0447 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u043b \u043f\u043b\u043e\u0434\u043e\u0442\u0432\u043e\u0440\u043d\u043e\u0435 \u0443\u0447\u0430\u0441\u0442\u0438\u0435 \u0432 \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0438 \u0440\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u043e-\u0431\u043e\u043b\u0433\u0430\u0440\u0441\u043a\u043e\u0433\u043e \u0441\u043e\u0442\u0440\u0443\u0434\u043d\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f.
Keywords:<\/em> mathematics; methodology; professor; collaboration<\/p>\n

\u00a0<\/p>\n

GENADII LUKANKIN: A MODEST PICTURE IN THE INTERIOR OF THE EPOCH<\/strong>
(on occasion of the 80-anniversary)<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> In the present year it is the 80-anniversary of Genadii Lavrovich Lukankin (1937 \u2013 2006), a famous scientist-mathematician (complex analysis of several variables, boundary value problems), outstanding specialist in the domain of secondary (general) and high-professional education, corresponding member of RAO. Genadii Lavrovich has provided a basis for Russian-Bulgarian fruitful collaboration in mathematical education.<\/p>\n

\u00a0<\/p>\n

Prof. Boris Tebiev, DSc
President
International Pedagogical Academy \u2013 Moskow (Russia)<\/p>\n

Dr. Alexander Lukankin, Assoc. Prof.
Vice-Rector
Moscow Regional Social-economy Institute \u2013 Moskow (Russia)<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

<\/a>\u0421\u041f\u041e\u041c\u0415\u041d \u0417\u0410 \u041f\u0420\u041e\u0424\u0415\u0421\u041e\u0420 \u0410\u041d\u0422\u041e\u041d \u0428\u041e\u0423\u0420\u0415\u041a<\/span><\/strong><\/p>\n

\u00a0<\/p>\n

\u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0430 \u0422\u0440\u0438\u0444\u043e\u043d\u043e\u0432\u0430
New Bulgarian University<\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> \u041d\u0430\u0441\u0442\u043e\u044f\u0449\u0430\u0442\u0430 \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442\u0430\u043b\u043d\u0430 \u043f\u0443\u0431\u043b\u0438\u043a\u0430\u0446\u0438\u044f \u043f\u0440\u0438\u043f\u043e\u043c\u043d\u044f \u0437\u0430 \u0435\u0434\u0438\u043d \u043e\u0442 \u0431\u0435\u043b\u0435\u0436\u0438\u0442\u0438\u0442\u0435 \u0434\u0435\u0439\u0446\u0438 \u043d\u0430 \u0431\u044a\u043b\u0433\u0430\u0440\u0441\u043a\u043e\u0442\u043e \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0441\u043b\u0435\u0434 \u041e\u0441\u0432\u043e\u0431\u043e\u0436\u0434\u0435\u043d\u0438\u0435\u0442\u043e \u2013 \u0447\u0435\u0448\u043a\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a \u0410\u043d\u0442\u043e\u043d \u0428\u043e\u0443\u0440\u0435\u043a. \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0435\u043d \u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u0435\u043d \u0434\u043e\u043a\u0443\u043c\u0435\u043d\u0442 \u043e\u0442 \u043b\u0438\u0447\u043d\u0438\u044f \u043c\u0443 \u0430\u0440\u0445\u0438\u0432 \u2013 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u0430 \u043f\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u0437\u0430 \u0434\u043e\u043b\u043d\u0438\u0442\u0435 \u043a\u043b\u0430\u0441\u043e\u0432\u0435 \u043d\u0430 \u0433\u0438\u043c\u043d\u0430\u0437\u0438\u0430\u043b\u043d\u0438\u0442\u0435 \u0443\u0447\u0438\u043b\u0438\u0449\u0430, \u043a\u043e\u044f\u0442\u043e \u0442\u043e\u0439 \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u0432\u0430 \u043d\u0430\u0439-\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e \u043f\u0440\u0435\u0437 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0442\u0435 \u0434\u0432\u0435 \u0434\u0435\u0441\u0435\u0442\u0438\u043b\u0435\u0442\u0438\u044f \u043d\u0430 XIX \u0432.
Keywords:<\/em> Czechs educational figures in Bulgaria; high school; geometry; geometric drawing<\/p>\n

\u00a0<\/p>\n

A MEMORY FOR PROFESSOR ANTON SHOUREK<\/strong><\/p>\n

\u00a0<\/p>\n

Abstract.<\/strong> The present documentary publication reminds of one of the outstanding figures in the Bulgarian education after the Liberation – the Czech mathematician Anton Shourek. Unknown document from his personal archive is presented \u2013 curriculum in geometry for the lower classes of the secondary school, which most probably has been developed during the last two decades of the 19th century.<\/p>\n

\u00a0<\/p>\n

Dr. Aleksandra Trifonova
New Bulgarian University \u2013 Sofia (Bulgaria)<\/p>\n

\u043d\u0430\u0433\u043e\u0440\u0435<\/a><\/p>\n

\n

\u00a0<\/p>","protected":false},"excerpt":{"rendered":"

CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418\u0412\u044a\u0440\u0445\u0443 \u0435\u0434\u0438\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0434\u043e\u043c\u0430\u0448\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0430 \u043d\u0430 \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [On a Model of the Homework in the Context of Self-Preparation in Mathematics Education] \/ \u041c\u0430\u0440\u0433\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Marga Georgieva, Diana Stefanova \u2013 \u0441\u0442\u0440.\/page 231 \u00a0 \u041d\u044f\u043a\u043e\u043b\u043a\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 […]<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[3486],"tags":[],"yoast_head":"\n"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\""\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430", \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"CONTENTS \/ \u0421\u042a\u0414\u042a\u0420\u0416\u0410\u041d\u0418\u0415 \u00a0 EDUCATIONAL MATTERS \/ \u041d\u0410\u0423\u0427\u041d\u041e-\u041c\u0415\u0422\u041e\u0414\u0418\u0427\u0415\u0421\u041a\u0418 \u0421\u0422\u0410\u0422\u0418\u0418\u0412\u044a\u0440\u0445\u0443 \u0435\u0434\u0438\u043d \u043c\u043e\u0434\u0435\u043b \u043d\u0430 \u0434\u043e\u043c\u0430\u0448\u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043a\u043e\u043d\u0442\u0435\u043a\u0441\u0442\u0430 \u043d\u0430 \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u043d\u0430\u0442\u0430 \u0440\u0430\u0431\u043e\u0442\u0430 \u0432 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u0435\u0442\u043e \u043f\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 [On a Model of the Homework in the Context of Self-Preparation in Mathematics Education] \/ \u041c\u0430\u0440\u0433\u0430 \u0413\u0435\u043e\u0440\u0433\u0438\u0435\u0432\u0430, \u0414\u0438\u0430\u043d\u0430 \u0421\u0442\u0435\u0444\u0430\u043d\u043e\u0432\u0430 \/ Marga Georgieva, Diana Stefanova \u2013 \u0441\u0442\u0440.\/page 231 \u00a0 \u041d\u044f\u043a\u043e\u043b\u043a\u043e \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043d\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430\u0442\u0430 […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2017-06-03T07:52:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2019-06-24T14:33:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/azbuki.bg\/wp-content\/uploads\/2012\/08\/components_com_docman_themes_default_images_icons_16x16_pdf.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\"},\"author\":{\"name\":\"\",\"@id\":\"\"},\"headline\":\"„\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430“, \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017\",\"datePublished\":\"2017-06-03T07:52:52+00:00\",\"dateModified\":\"2019-06-24T14:33:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\"},\"wordCount\":2012,\"publisher\":{\"@id\":\"https:\/\/azbuki.bg\/#organization\"},\"articleSection\":[\"\u0421\u044a\u0434\u044a\u0440\u0436\u0430\u043d\u0438\u0435 \u043d\u0430 \u0441\u043f. \\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\", 2017 \u0433.\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\",\"url\":\"https:\/\/newspaper.azbuki.bg\/matematics\/matharticles2016-2\/3-lxx-2017\/\",\"name\":\"\\\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0442\u0438\u043a\u0430\\\", \u043a\u043d\u0438\u0436\u043a\u0430 3, \u0433\u043e\u0434\u0438\u043d\u0430 LX, 2017 - 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